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On the Existence and Uniqueness of Solutions to Rough Fractional Stochastic Differential Equations | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 1، اردیبهشت 2026، صفحه 31-44 اصل مقاله (203.22 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2025.86744.1194 | ||
| نویسندگان | ||
| Farshid Mehrdoust* 1؛ Arezou Karimi2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan | ||
| 2Mathematical Science, Applied Mathematics | ||
| چکیده | ||
| Precise modeling of financial asset volatility is significant for robust risk management and derivative pricing. Recent scholarly investigations have demonstrated a significant interest in employing stochastic processes with short-term memory for this purpose. Consequently, rigorous examination of the existence and uniqueness of solutions for these processes assumes critical importance. This study commences with the precise definition of a fractional operator for $H \in(0, \frac{1}{2})$. Subsequently, the finiteness of the second-order moment of the Itô-Skorokhod integral is meticulously investigated, utilizing the aforementioned operator, specifically within the range of $H \in(0, \frac{1}{2})$. Ultimately, leveraging this moment and rigorously applying Lipschitz and linear growth conditions, and through the application of Gronwall's inequality, the existence and uniqueness of solutions for stochastic differential equations with short-term memory are definitively established. | ||
| کلیدواژهها | ||
| Fractional Brownian motion؛ Wiener integral؛ Stochastic differential equations؛ Lipschitzian condition؛ Gronwall' s inequality | ||
| مراجع | ||
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